The goal of this project is to develop improved statistical methods for toxicology and laboratory studies. Work has focused on developing flexible statistical methods for multivariate data, which avoid restrictive parametric assumptions, while enabling learning about changes in the distribution of biologic responses with dose and other factors. We have made substantial progress through the use of new Bayesian semiparametric methods. One class of methods were developed for multiple event time data, such as tumor appearance times in photococarcinogenicity and chemoprevention experiments. The proposed approach allows the distribution of tumor susceptibility among animals to vary dynamically with age and dose. The results were applied to chemoprevention data, allowing insights not possible with existing models that do not allow dynamic changes with age. We also developed a class of density regression methods, which allow latent traits underlying multiple responses to change flexibly with covariates, such as genetic and environmental factors. For example, the latent trait corresponds to cell-specific DNA damage in comet assay studies, which can measure DNA damage only indirectly through multiple surrogates. Our proposed approach allows heterogeneity among cells and individuals in the effect of exposure, and can be used broadly to assess evidence of sensitive sub-populations. An additional method was developed motivated by the problem of assessing body weight and tumor relationships using data from toxicology and carcinogenicity studies. The analysis used a new multivariate adaptive regression splines method.